lecture 3: enzyme kinetics km dan vmax i. introduction 1. basic enzyme reactions 1. enzyme...

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    To succumb is healthier than to conquer, as we may calm down and developaffection and love, as well as avoid emotion, angriness or madness, and hate


    After the completion of the lecture and masteringthe lecture materials, students will be able to1. to explain enzyme substrate interaction in the

    conversion of substrate to product2. to explain the order of chemical reactions3. to explain enzyme kinetics particularly the rate of

    reactions as a function of substrate concentration4. to calculate KM and Vmax of reactions catalyzed by

    enzymes5. to explain characteristics of enzymes based kinetic

    analysis of enzymatic reactions

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    1. Definition2. Basic Enzyme

    Reactions3. The rate of reaction


    Hypothesis2. The "Induced Fit"



    1. The formation of ESComplex

    2. Steady-StateAssumption

    3. Initial VelocityAssumption

    4. Total EnzymeIV. PENETUAN KM DAN


    I. INTRODUCTION1. Basic Enzyme Reactions

    1. Enzyme kinetics is the study of thechemical reactions that are catalyzedby enzymes or the study of the rates ofenzyme-catalyzed reactions.

    The branch of chemistry which deals with the ratesof chemical processes is known as chemical kinetics

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    2. Enzymes, functioning as catalysts, increase thespeed of a chemical reactions, and are not used upin the reactions.The basic enzymatic reaction can be represented asfollowsS + E P + E (1)where E = enzyme, S = substrate, and P = product ofthe reaction.

    3. A theory to explain the catalytic action of enzymeswas developed by Savante Arrhenius in 1888, aSwedish chemist. He proposed that the substrate (S)and enzyme (E) formed some intermediatesubstance known as the enzyme substrate complexas shown below.S + E ES (2)

    4. If this reaction is combined with the original reactionequation (1), the following results:S + E ES P + E (3)

    5. The existence of an intermediate enzyme-substratecomplex has been demonstrated in the laboratory, forexample, using catalase and a hydrogen peroxidederivative.

    6. At Yale University, Kurt G. Stern in 1937 observedspectral shifts in catalase as the reaction it catalyzedproceeded.- This experimental evidence indicates that the

    enzyme first unites in some way with the substrateand then returns to its original form after thereaction is concluded.

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    2. The rate of reaction1. The rate of reaction (V) is the quantity of substrate

    (S) converted to product, or the amount product (P)produced per unit time.

    2. Reactions follow zero order kinetics whensubstrate concentrations are high.- Zero order means there is no increase in the

    rate of the reaction when more substrate isadded.Zero orderSP

    Where V is the rate (velocity) of reaction









    Order Rate Commentszero k rate is independent of substrateconcentrationfirst k[S] rate is proportional to the first power ofsubstrate concentration

    second k[S][S]=k[S]2 rate is proportional to the square of the

    substrate concentration

    k[S1][S2]rate is proportional to the first power ofeach of two reactants

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    The rate of enzymatic reaction is influenced bythe interaction of enzyme and substrate.

    The two types of interaction between enzymeand substrate1. Lock and Key" Hypothesis2. The "Induced Fit" Hypothesis

    1. "Lock and Key" Hypothesis- Emil Fischer in 1890 proposed "Lock and Key"


    - The shape, or configuration (form in space), of theactive site is especially designed for the specificsubstrate involved.

    - As the active site is made up of protein, the formof active site in space (configuration) isdetermined by the amino acid sequence of theenzyme in the active site.

    active site


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    - It is also important that the native configuration of theentire enzyme molecule must be intact for the activesite to have the correct configuration.

    - In such a case, the substrate then fits into the activesite of the enzyme in much the same way as a keyfits into a lock.

    - Enzyme examples follow the lock and key hypothesisare RNase A, cyclophilin A, and dihydrofolatereductase (Sullivan & Holyoak, 2008)

    2. The "Induced Fit" Hypothesis- Enzymes are highly flexible, conformationally

    dynamic molecules.- Many of their remarkable properties, including

    substrate binding and catalysis, are due to theirstructural pliancy.

    - Realization of the conformational flexibility ofproteins led Daniel Koshland to hypothesize that thebinding of a substrate (S) by an enzyme is aninteractive process.

    - The shape of the enzyme's active site is actuallymodified upon binding S, in a process of dynamicrecognition between enzyme and substrate aptlycalled induced fit.

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    ATP lyaseorATPase

    Transition conformation

    In essence, substrate binding alters the conformationof the protein, so that the protein and the substrate "fit"each other more precisely.

    The process is truly interactive in that the conformationof the substrate also changes as it adapts to theconformation of the enzyme. An example of enzymefollow Induced-fit hypothesis is Rubisco.

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    Induced Fit Model

    Hexokinase has a large induced fit motion that closesover the substrates adenosine triphosphate (ATP) andxylose.

    Hexokinase catalyzesthe following reaction.

    Gucose + ATP Glucose-6P + ADP

    Binding sites in blue,substrates in blackand Mg2+ cofactor inyellow. (PDB: 2E2N ,2E2Q)

    III. MICHAELIS-MENTEN MODELLeonor Michaelis and Maud L. Menten proposed ageneral theory of enzyme action in 1913 whilestudying the hydrolysis of sucrose catalyzed by theenzyme invertase.

    1. The formation of ES Complex Their theory was based on the assumption that the

    enzyme (E) and its substrate (S) associate reversiblyto form an enzyme-substrate complex, ES

    k1E + S ES E + Pk2k3k4

    E = Enzyme, S = Substrate, P = Product, ES = Enzyme-Substratecomplex , and k1, k2, k3 & k4 = rate constants. k4 is very small andignored

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    For instance, the breakdown of sucrose toglucose and fructose through a hydrolysisreaction catalyzed by sucrase (invertase)

    Sucrose + H20 Glucose + Fructose If environmental factors

    are constant, the rate ofproduct formation(reaction rate of velocity,V) is dependent uponthe concentration ofenzyme and substrate

    - [E] = enzyme concentration- [S] = substrate concentration

    Effect of [E] to study the effect of increasing the [E] upon the

    reaction rate, the substrate must be present in anexcess amount so that the reaction is independentof the [S].[S][E]

    The formation of productproceeds at a rate which islinear with time.

    Any change in the amount ofproduct formed over a specified



    [S] is constant

    period of time is dependent upon the level ofenzyme present.

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    The reactions with the rates independent ofsubstrate concentration but equal to someconstant k are said to be "zero order" .

    The influence of [S] The concentration of substrate [S] greatly

    influences the rate of product formation (thevelocity of a reaction, V)- Studying the effects of [S] on the velocity of a

    reaction is complicated by the reversibility of enzymereactions, e.g. conversion of product back tosubstrate

    - To overcome this problem, initial velocity (V0)measurements are used. At the start of a reaction, [S] is in large excess of [P] [S][P]

    thus the initial velocity of the reaction (V0) will bedependent on substrate concentration [S]

    When initial velocity is plotted against [S], a hyperboliccurve is found and characterized by an approximatelyconstant maximum of reaction rate (Vmax)

    Low [S]

    50% [S]

    High [S]Saturating [E]

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    Vmax represents the maximum reaction velocity This occurs at [S] >> E, and all available enzyme is

    "saturated" with bound substrate, meaning only theES complex is present

    The association/dissociation of ES complex isassumed to be a rapid equilibrium, and theenzyme:substrate dissociation constant is Ks.At equilibrium,k2[ES] = k1[E][S]and






    2. Steady-State Assumption The interpretations of Michaelis and Menten were

    refined and extended in 1925 by Briggs andHaldane, by assuming [ES] quickly reaches aconstant value in such a dynamic system.

    That is, ES is formed rapidly from E + S, anddisappears by its two possible fates- dissociation to regenerate E + S, and- reaction to form E + P

    This assumption is termed the steady-stateassumption and is expressed as



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    3. Initial Velocity Assumption Enzymes accelerate the rate of the reverse

    reaction as well as the forward reaction, then theconversion of E+P to ES or k4[E][P] = k3[ES]

    If we observe only the initial velocity for thereaction immediately after E and S are mixed inthe absence of P, the rate of any back reaction isnegligible.

    Therefore, k4[E][P] = 0 as [P] is essentially 0which gives

    k1E + S ES E + Pk2k3


    Given such simplification, the system described byequation above is analyzed in order to describethe initial velocity V as a func